A 4 \(\times\) 1 multiplexer with two selector lines is used to realize a Boolean function \( F \) having four Boolean variables X, Y, Z and W as shown below. \( S_0 \) and \( S_1 \) denote the least significant bit (LSB) and most significant bit (MSB) of the selector lines of the multiplexer respectively. \( I_0, I_1, I_2, I_3 \) are the input lines of the multiplexer.
The canonical sum of product representation of F is
A 4 \(\times\) 1 multiplexer with two selector lines is used to realize a Boolean function \( F \) having four Boolean variables X, Y, Z and W as shown below. \( S_0 \) and \( S_1 \) denote the least significant bit (LSB) and most significant bit (MSB) of the selector lines of the multiplexer respectively. \( I_0, I_1, I_2, I_3 \) are the input lines of the multiplexer.
The canonical sum of product representation of F is
Show Hint
- \( F(X, Y, Z, W) = \sum m(0, 1, 3, 14, 15) \)
- \( F(X, Y, Z, W) = \sum m(0, 1, 3, 11, 14) \)
- \( F(X, Y, Z, W) = \sum m(2, 5, 9, 11, 14) \)
- \( F(X, Y, Z, W) = \sum m(1, 3, 7, 9, 15) \)
The Correct Option is B
Solution and Explanation
Step 1: The multiplexer configuration corresponds to the sum of minterms where the output is 1.
Step 2: After checking the input combinations, we conclude that the canonical sum of products representation is \( F(X, Y, Z, W) = \sum m(0, 1, 3, 11, 14) \).
Final Answer:
(B) \( F(X, Y, Z, W) = \sum m(0, 1, 3, 11, 14) \)
Top Questions on Multiplexers
The figure shows a 4-to-1 multiplexer. The inputs are connected as:
$I_0 = 1$, $I_1 = 0$, $I_2 = 1$, $I_3 = y$.
The select lines are $S_1 = x$ and $S_0 = z$.
Find the Boolean function $f(x,y,z)$.
- GATE EC - 2026
- Digital Electronics
- Multiplexers
- Minimum number of 2:1 Multiplexers required to design a 16:1 Multiplexer is?
- CUET (PG) - 2025
- Computer Science
- Multiplexers
- The following multiplexer gives the logic gate of a/an _____
- It is possible for an enable or strobe input to undergo an expansion of two or more MUX ICs to the digital multiplexer with the proficiency of large number of:
- A 32:1 MUX can can be designed using:
- CUET (PG) - 2023
- Digital Electronics
- Multiplexers
Questions Asked in GATE IN exam
- A car is moving collinearly with a laser beam emitted by a transceiver. A laser pulse emitted at \( t = 0 \) s is received back by the transceiver 100 ns (nanoseconds) later after reflection from the car. A second pulse emitted at \( t = 0.1 \) s is received back 90 ns later. Given the speed of light is \( 3 \times 10^8 \) m/s, the average speed of the car in this interval is _________
- GATE IN - 2022
- Displacement (linear and angular)
- Consider the function \( f(z) = \frac{1}{(z+1)(z+2)(z+3)} \). The residue of \( f(z) \) at \( z = -1 \) is _________.
- GATE IN - 2022
- Residue Theorem
- In the circuit shown, the load is driven by a sinusoidal ac voltage source \( V_1 = 100 \angle 0^\circ \, \text{V} \) at 50 Hz. Given \( R_1 = 20 \, \Omega \), \( C_1 = \left(\frac{1000}{\pi}\right) \, \mu\text{F} \), \( L_1 = \left(\frac{20}{\pi}\right) \, \text{mH} \), and \( R_2 = 4 \, \Omega \), the power factor is _________ (round off to one decimal place)
- GATE IN - 2022
- Transient analysis of RLC circuits with ac excitation
- In the circuit shown, the capacitance \( C_0 = 10 \, \mu\text{F} \) and inductance \( L_0 = 1 \, \text{mH} \) and the diode is ideal. The capacitor is initially charged to 10 V and the current in the inductor is initially zero. If the switch is closed at \( t = 0 \, \text{s} \), the voltage \( V_C(t) \) (in volts) across the capacitor at \( t = 0.5 \, \text{s} \) is _________ (round off to one decimal place)
- GATE IN - 2022
- Diodes: Characteristics and Applications
- In the circuit shown, the switch is initially closed. It is opened at \( t = 0 \, \text{s} \) and remains open thereafter. The time (in milliseconds) at which the output voltage \( V_{\text{out}} \) becomes LOW is _________ (round off to three decimal places).
- GATE IN - 2022
- Sample and hold circuits